Shin Kiriki, Hiroshi Kokubu, and Ming-Chia Li,

An index changing bifurcation creating heterodimensional cycles,

submitted (revised version)

Zin Arai, William Kalies, Hiroshi Kokubu, Konstantin Mischaikow, Hiroe Oka, and Pawel Pilarczyk,

A databases schema for the analysis of global dynamics of multiparameter systems,

to appear in SIAM Journal on Applied Dynamical Systems.

Zin Arai, Hiroshi Kokubu, and Pawel Pilarczyk,

Recent development in rigorous computational methods in dynamical systems,

to appear in Japan Journal of Industrial and Applied Mathematics.

Sarah Day, Hiroshi Kokubu, Stefano Luzzatto, Konstantin Mischaikow, Hiroe Oka, and Pawel Pilarczyk,

Quantitative hyperbolicity estimates in one-dimensional dynamics,

Nonlinearity 21 (2008), 1967-1987.

Hiroshi Kokubu, Daniel Wilczak, and Piotr Zgliczyñski,

Rigorous verification of the cocoon bifurcation in the Michelson system,

Nonlinearity 20 (2007), 2147-2174.

Marcio Gameiro, Tomas Gedeon, William Kalies, Hiroshi Kokubu, Konstantin Mischaikow, and Hiroe Oka,

Topological horseshoes of traveling waves for a fast-slow predator-prey system,

Journal of Dynamics and Differential Equations 19 (2007), 623-654 (Special Issue dedicated to Prof. Pavol Brunovsky's 70th birthday).

Tomas Gedeon, Hiroshi Kokubu, Konstantin Mischaikow, and Hiroe Oka,

Conley index for fast-slow systems II: Multi-dimensional slow variable,

Journal of Differential Equations 225 (2006), 242-307.

Freddy Dumortier, Santiago Ibañez, and Hiroshi Kokubu,

Cocoon bifurcation in three dimensional reversible vector fields,

Nonlinearity 19 (2006), 305-328.

Hiroshi Kokubu and Robert Roussarie,

Existence of a singularly degenerate heteroclinic cycle in the Lorenz system and its dynamical consequences, Part I,

Journal of Dynamics and Differential Equations, 16 (2004), 513-557 (Special Issue dedicated to Prof. Shui-Nee Chow's 60th birthday).

Tomas Gedeon, Hiroshi Kokubu, Konstantin Mischaikow, and Hiroe Oka,

Chaotic solutions in slowly varying perturbations of Hamiltonian systems with applications to shallow water sloshing,

Journal of Dynamics and Differential Equations, 14 (2002), 63-84.

Ale Jan Homburg, Hiroshi Kokubu, and Vincent Naudot,

Homoclinic-doubling cascades,

Archiev for Rational Mechanics and Analysis, 160 (2001), 195-243

Freddy Dumortier, Santiago Ibanez and Hiroshi Kokubu,

New aspects of the unfolding of the nilpotent singularity of codimension three,

Dynamical Systems: an International Journal, 16 (2001), 63-95.

Hiroshi Kokubu

On transition matrices,

EQUADIFF99, Proceedings of the International Conference on Differential Equations, Berlin, Germany 1-7 August 1999, World Scientific, 2000, pp.219-224.

Freddy Dumortier and Hiroshi Kokubu

Chaotic dynamics in Z_2-equivariant unfoldings of codimension 3 singularities of vector fields in R^3,

Ergodic Theory and Dynamical Systems, 20 (2000), 85--107.

Tomas Gedeon, Hiroshi Kokubu, Konstantin Mischaikow, Hiroe Oka, and James Reineck,

Conley index for fast-slow systems I: One-dimensional slow variable,

Journal of Dynamics and Differential Equations, 11 (1999), 427--470.

Hiroshi Kokubu, Konstantin Mischaikow, and Hiroe Oka,

Directional transition matrix,

in "Conley Index Theory" (Eds. K. Mischaikow, M. Mrozek, P. Zgliczy\'nski), Banach Center Publication, Vol. 47, 1999, Warsaw, Poland, pp. 133-144.

Hiroshi Kokubu, Konstantin Mischaikow, Yasumasa Nishiura, Hiroe Oka, and Takeshi Takaishi,

Connecting orbit structure of monotone solutions in the shadow system,

Journal of Differential Equations, 140 (1997), 309-364.

Hiroshi Kokubu and Vincent Naudot,

Existence of infinitely many homoclinic doubling bifurcations from some codimension three homoclinic orbits,

Journal of Dynamics and Differential Equations, 9 (1997), 445-462.

Hiroshi Kokubu, Hiroe Oka and Duo Wang

Linear grading function and further reduction of normal forms,

Journal of Differential Equations, 132 (1996), 293--318.

Hiroshi Kokubu, Motomasa Komuro, and Hiroe Oka,

Multiple homoclinic bifurcations from orbit-flip, I: Successive homoclinic doublings,

International Journal of Bifurcations and Chaos, 6 (1996), 833-850 (Special issue dedicated to Professor L. P. Shil'nikov's 60th birthday).

Hiroshi Kokubu, Konstantin Mischaikow, and Hiroe Oka,

Existence of infinitely many connecting orbits in a singularly perturbed ordinary differential equations,

Nonlinearity, 9 (1996), 1263-1280.

Freddy Dumortier, Hiroshi Kokubu, and Hiroe Oka,

A degenerate singularity generating geometric Lorenz attractors,

Ergodic Theory and Dynamical Systems, 15 (1995), 833-856.

Ale Jan Homburg, Hiroshi Kokubu, and Martin Krupa,

The cusp horseshoe and its bifurcations from inclination-flip homoclinic orbits,

Ergodic Theory and Dynamical Systems, 14 (1994), 667-693.

Masashi Kisaka, Hiroshi Kokubu, and Hiroe Oka,

Bifurcations of N-homoclinic and N-periodic orbits in vector fields,

Journal of Dynamics and Differential Equations, 5 (1993), 305-357.

Hiroshi Kokubu,

A construction of three-dimensional vector fields which have a codimension two heteroclinic loop at Glendinning-Sparrow T-point,

Zeitschrift fur angewandte Mathematik und Physik, 44 (1993), 510-536.

Hiroshi Kokubu and Hiroe Oka,

Bifurcation of Lorenz-like attractors from a degenerate vector field singularity,

in "Chaotic Dynamical Systems" (Ed., S. Ushiki), Advanced Series in Dynamical Systems, Vol. 13, (1993), pp. 29-35, World Scientific.

Masashi Kisaka, Hiroshi Kokubu, and Hiroe Oka,

Supplement to homoclinic doubling bifurcation in vector fields,

in "Dynamical Systems", (Eds. R. Bamon, R. Labarca, J. Lewowicz, and J. Palis, Jr.), Pitman Research Notes in Mathematics, Vol. 285, (1993), pp. 92-116, Longman Scientific and Technical.

Hiroshi Kokubu,

Heteroclinic bifurcations associated with different saddle indices,

in Proceedings of the International Conference "Dynamical Systems and Related Topics", Advanced Series in Dynamical Systems, Vol. 9 (Ed. K. Shiraiwa), (1991), pp. 236-260, World Scientific.

Hiroshi Kokubu, Yasumasa Nishiura, and Hiroe Oka,

Heteroclinic and homoclinic bifurcations in bistable reaction diffusion systems,

Journal of Differential Equations, 86 (1990), 260-341.

Hiroe Oka and Hiroshi Kokubu,

Versal unfoldings of constrained systems of corank 1,

in "Proceedings of the International Conference on Bifurcation Theory and its Numerical Analysis, Xi'an, 1988" (Eds., L. Kaitai, J. Marsden, M. Golubitsky and G. Iooss), (1989), pp. 378-384, Xi'an Jiaotong University Press.

Hiroshi Kokubu,

On a heteroclinic bifurcation of vector fields,

in "Proceedings of the International Conference on Bifurcation Theory and its Numerical Analysis, Xi'an, 1988", (Eds., L. Kaitai, J. Marsden, M. Golubitsky and G. Iooss), (1989), pp. 277-284, Xi'an Jiaotong University Press.

Hiroshi Kokubu, Yasumasa Nishiura, and Hiroe Oka,

An application of hetero- and homoclinic bifurcation to bistable reaction diffusion systems,

in "Stability Theory and Related Topics in Dynamical Systems" (Eds., K. Shiraiwa and G. Ikegami),

Advanced Series in Dynamical Systems, Vol. 6, (1989), pp. 86-107, World Scientific.

Leon O. Chua and Hiroshi Kokubu,

Normal forms for nonlinear vector fields - Part I: Theory and algorithm,

IEEE Transaction on Circuits and Systems, 35 (1988), 863-880;

Normal forms for nonlinear vector fields - Part II: Applications,

IEEE Transaction on Circuits and Systems, 36 (1989), 51-70.

Hiroshi Kokubu,

Homoclinic and heteroclinic bifurcations of vector fields,

Japan Journal of Applied Mathematics, 5 (1988), 455-501.

Hiroshi Kokubu,

On a bifurcation of heteroclinic orbits,

in "Dynamical Systems and Applications", (Ed. N. Aoki), Advanced Series in Dynamical Systems, Vol. 5, (1987), pp. 169-181, World Scientific.

Hiroe Oka and Hiroshi Kokubu,

Versal unfolding of constrained systems,

in "Dynamical Systems and Applications", (Ed. N. Aoki), Advanced Series in Dynamical Systems, Vol. 5, (1987), pp. 159-167, World Scientific.

Hiroshi Kokubu,

On a codimension 2 bifurcation of heteroclinic orbits,

Proceedings of Japan Academy, 63 (1987), 298-301.

Hiroe Oka and Hiroshi Kokubu,

An approach to constrained equations and strange attractors,

in "Patterns and Waves - Qualitative Analysis of Nonlinear Differential Equations'', (Eds. H. Fujii, M. Mimura and T. Nishida), Stud. Math. Appl., Vol. 18, (1986), pp. 607-630, Kinokuniya/North-Holland.

Hiroe Oka and Hiroshi Kokubu,

Normal forms for constrained equations and their applications to strange attractors,

in "Proceedings of 24th IEEE Conference on Decision and Control, Ft. Lauderdale, Florida", (1985), pp. 461-466.

Hiroe Oka and Hiroshi Kokubu,

Constrained Lorenz-like attractors,

Japan Journal of Applied Mathematics, 2 (1985), 495-500.

Hiroshi Kokubu,

Normal forms for parametrized vector fields and its applications to bifurcations of some reaction diffusion equations,

Japan Journal of Applied Mathematics, 1 (1984), 273-297.

Shigehiro Ushiki, Hiroe Oka, and Hiroshi Kokubu,

Existence d'attracteurs etranges dans le d'eploiement d'une singularite degeneree d'un champ de vecteuers invariant par translation,

Comptes Rendus l'Academie des Sciences, Paris, Serie I, Mathematiques, t. 298 (1984), 39-42.